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  • The mean of the following distribution is 50.Find the value of a and hence the frequencies of 30 and 70.

The mean of the following distribution is 50.

x f
10 17
30 5a+3
50 32
70 7a-11
90 19

Find the value of a and hence the frequencies of 30 and 70.

Answers (1)

a = 5, f_{30} = 28, f_{70} = 24

The frequency distribution table is as follows:

x_{i} f_{i} f_{i}x_{i}
10 17 170
30 5a+3 150a+90
50 32 1600
70 7a-11 490a-770
90 19 1710
Total 60+12a 2800+640a

Mean =\frac{\sum f_{i}x_{i}}{\sum f_{i}}

\frac{50}{1}=\frac{2800+640a}{60+12a}

[Cross multiply]

50\left ( 60+12a \right )=2800+640\; a

3000+600a=2800+640a

3000 - 2800 = 640a - 600a

200 = 40a

\frac{200}{40}=a

a=5

\\f_{30} = 5a + 3 \\ f_{30} = 5(5) + 3 = 28\\ f_{70} = 7a - 11\\ f_{70} = 7(5) -11\\ f_{70} = 35 - 11 = 24

Posted by

infoexpert23

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